Profit Efficiency among Dairy Farmers in Southern India: An Application of Stochastic Frontier Profit Function

Self-sufficiency in milk Production has been one of the critical issues in South Indian states due to insufficient multi-cut green fodder crops in time and a lack of knowledge about unconventional fodder sources.The study area’s dairy farmers successfully selected an optimal set of livestock inputs consistent with relative dairy product prices. Although necessary, technical efficiency studies are insufficient to explain why dairy farmers exit the dairy sector (Bahta et al., 2021).
       
Small dairy farms in Andhra Pradesh confront different production risks due to increasing dependence on external fodder suppliers, which usually undermines the farm’s profitability (Drews et al., 2020). The profitability and resource efficiency of dairy farms depends on various aspects such as the quality of fodder, adoption of technology etc. (Toma et al., 2013). This scenario provides little understanding of the profit efficiency elements in the study area and suggests the need for additional research, particularly on revenue components (Adenuga et al., 2018). The hypothesis in the present study is that optimal use of inputs could contribute to improvements in dairy productivity and efficiency in profit. Due to this, the present study was carried out to gain insight into the performance efficiency of dairy farmers in Southern India, for which the profit efficiency of dairy farmers across different herd size categories in the study area was estimated,and an inefficiency model to identify socio-economic factors that affect variations in profit efficiency was constructed.

The research was carried out at Dr Rajendra Prasad Central Agricultural University, Pusa, Samastipur Bihar, during 2019-21 as a part of Doctoral research by the first author. The study area was the Southern Indian states of Andhra Pradesh (623 gm/day), Karnataka (344 gm/day), and Tamil Nadu (322 gm/day),which were selected on the basis of the highest per capita availability of milk during 2020-21 (Fig 1). One district per state was selected based on cattle population; thus,Chittoor, Belgaum and Villupuram districts were selected from Andhra Pradesh, Karnataka and Tamil Nadu, respectively. One mandal and two villages from each mandal were randomly selected from each district.Further, 240 respondents, i.e. eighty from each state,were selected (Table1). The chosen respondents were post-stratified into three herd-size categories, namely Small (1-3 milch animals), Medium (4-6 milch animals), and Large (7 and above milch animals) using the Cumulative Square Root Frequency Method.




       
To the study, there are many factors which influence the profit efficiency of dairy farms. But, major factors like farmer’s practices, dairy breeds, fodder, feeding system, veterinary services, market size, distance to town, education of farmers and age of farmers were thought to influence the profit efficiency of dairy farms in the study area. Conceptual framework on factors influencing profit efficiency of dairy farmer was shown in the Fig 2.

​
 
The Stochastic Profit Frontier Function
 
Two aspects of production efficiency that are typically examined are technical and allocative efficiency.Any faults in production choice are supposed to convert into decreased profits or revenue for producers under the profit function method, which blends technical and allocative efficiency ideas in the profit relationship (Ali et al., 1994). As a result, profit efficiency refers to a farm’s ability to generate the most profit possible given the pricing of variable inputs and the quantities of fixed elements on that farm. The loss of profit from not operating on the frontier means “profit inefficiency”(Ali & John, 1989). The inefficiency effects might be described as a linear function of explanatory factors, indicating farm-specific characteristics (Battese and Coelli, 1995). The benefit of this model is that it enables a single-stage estimation technique that can estimate efficiency scores particular to farms as well as the factors causing efficiency differences amongst dairy farmers. The Battese and Coelli (1995) model is used to obtain profit inefficiencies by postulating a profit function approach that is assumed to act in a manner consistent with the stochastic frontier idea. We used the OLS method in the second stage to regress profit inefficiencies obtained in stochastic frontier profit function on socio-economic factors. The definition of the stochastic profit function is: where,
pi  = Normalized profit of the i-th farm defined as gross revenue less variable cost, divided by farm-specific output price.
Pij= Price of j-th variable input faced by the i th farm divided  by the output price.
Zik = Level of the k-th fixed factor on the i th farm.
x i= Error term. 
i =1,..,n, number of farms in the sample.
The error term îi is assumed to behave in a manner consistent with the frontier concept, i.e.
  Where,
vi’s = Assumed to be independently and identically distributed two-sided error terms and independent of ui’s.
ui’s = Non-negative random variables associated with the inefficiency in production.
The profit efficiency of farm ‘i’ in the context of the stochastic frontier profit function is: Where,
E = Expectation operator.
       
The unknown parameters were estimated using maximum likelihood, and the stochastic frontier and inefficiency impact functions were also evaluated at the same time.The likelihood function was expressed in terms of the variance parameters,        
The Cobb- Douglas functional form of stochastic frontier profit function was expressed as,
  Where,
p* = Normalized profit (`).
P1 = Normalized price of green fodder (`).
P2 = Normalized price of dry fodder (`).
P3 = Normalized price of concentrate (`).
P4 = Normalized wage of labour (`).
P5 = Normalized fee of veterinary services (`).
Z1 = Herd size (number).
Z2 = Farm cost used (`).
Now, the inefficiency model uiis defined as:
  Where,
W1 = Age of the dairy farm head (years).
W2 = Education of the dairy farm head
W3 = Family labour (in numbers).
W4 = Herd size (in numbers).
W5 = Herd composition (ratio).
W6 = Experience in dairy farming (in years).
       
Herd composition implies the ratio ofthe total number of crossbred cows to the total herd size.
 
Estimation
 
FRONTIER 4.1 (Coelli, 1996) software was used to obtain maximum likelihood estimates of the stochastic Cobb-Douglas frontier profit function and profit inefficiency model.

a) Profit Efficiency Model
 
Maximum Likelihood Estimates of Parameters of Stochastic Profit Frontier Function
 
As evident from Table 2, overall, prices of green fodder(0.1873), concentrate (0.1072), veterinary service rate (0.0569), and herd size (0.7545) had a positive and significant impact on profits.At the same time, dry fodder price (-0.0277) and labour wage (-0.1652) negatively and significantly impacted profit. Finally, it was observed that a positive effect of green fodder and concentrate is reasonable when their prices increase; farmers will only feed the required quantity of green fodder and concentrate to their cattle so that overall cost decreases, thereby increasing profits. It is possible to increase the milk yield of animals by feeding them with green fodder and concentrate. Meena et al., (2012), Kumari and Malhotra (2018) and Acharya et al., (2021) all reported similar findings, indicating that feeding concentrate to animals increases milk yield, implying higher profits. Farmers’ milk yields are reduced when they use dry fodder, resulting in lower profits (Aquino et al., 2020; Kumari et al., 2020; Acharya et al., 2021). Hence, profit has a negative relationship with dry fodder. Profit was negatively associated with labour wages because increased labour hours raise labour costs, lowering profits. This is consistent with previous research by Kumari et al., (2020) and Acharya et al., (2021). Gamma must be a positive integer between 0 and 1. If _¡=0, inefficiency is absent, and _¡=1 random noise is absent. The estimated gamma value was close to one in all farmer herd size categories. It significantly differed from 0, implying that there were inefficiencies among the dairy farmers. Overall, the value was 0.7581, indicating that 75.81 per cent of the variation in actual profit from the frontier profit was caused by differences in the farmer’s practices in milk production rather than random noise, whereas it was 99.99 per cent, 90.19 percent, and 93.43 percent, respectively, in the small, medium, and large herd size categories. Nganga et al., (2010), Bardhan and Sharma (2013), Kaka et al., (2016), Kumari et al., (2020), Lal et al., (2020), Singh et al., (2012) and Acharya et al., (2021) all reported similar findings. The specified distributional assumptions of the composite error term’s fitness and accuracy are shown by the value of estimated s² which was found to be significant in all dairy farmer categories, i.e.small (0.3223), medium (0.1986), large (0.1061) and overall (0.1390).



Frequency Distribution of Profit Efficiency of Dairy Farmers

A perusal of Table 3 revealed that in the case of the small herd size category, profit efficiencies ranged between 36.11 to 90.66 per cent, with a mean profit efficiency of 59.42 per cent, respectively. While in the case of the medium herd size category, profit efficiencies ranged from 58.51 to 99.98 per cent, with a mean profit efficiency of 79.06 per cent, respectively. In the large herd size category, profit efficiencies ranged from 68.37 to 97.74 per cent, with a mean profit efficiency of 88.91 per centrespectively.


       
Overall, the mean profit efficiency was found to be 58.65 per cent, which varied between 32.50 to 89.61 per cent respectively. This implies that 40.58 per cent, 20.94 per cent, 11.09 per cent and 41.35 per cent of profit efficiency in the case of small, medium, large and overall dairy farmers was lost because of economic inefficiency. Farmers can fill this gap by improving technical and allocative efficiency (Nganga et al., 2010). It was also observed that mean profit efficiency increased as herd size increased. This resulted from the fact that as herd size increased, milk output also increased, thereby increasing the profitability of dairy farms. This is in agreement with the findings of Kumari et al., (2020) and Acharya et al., (2021). Overall, most dairy farmers in the study area had profit efficiencies ranging from 50 to 60 per cent (70).The maximum number of dairy farmers had their profit efficiencies in the range of 50 to 60 per cent in case of small, 70 to 80 per cent in case of medium and 90 to 100 per cent in case of large dairy farmers, with the numbers being 34, 21 and 29, respectively.

Box and Whisker plot analysis
 
We conducted a box and whisker plot analysis of the profit efficiency of dairy farms by herd size categories (Fig 3).Overall, the median was 57.67, which was highest for the large category (93.65), followed by medium (79.08) and least for small herd size category (56.70). It was also found that overall, the inter-quartile range (IQR) was 16.85, which varied from 10.89 for the large category, 16.52 for the medium category, to 17.28 for the small category respectively. The vertical length of the Box and whisker was found to be highest for the small category, followed by the medium category and least for the large herd size category, respectively, indicating that dairy farms of the small herd size category experienced the highest variation in efficiency score, followed by medium category and least in case of large category. Similar findings were reported by Acharya et al., (2021). The mean profit efficiency in the case of medium and large herd size categories ranges from 80 to 90 per cent, but it was around 60 per cent in the case of small herd size categories. It can thus be inferred that most dairy farmers of all categories have profit efficiency in the range of 45 to 90 per cent.



b) Profit Inefficiency Model

Profit inefficiency values obtained from stochastic frontier profit function were regressed on factors like age, education, family labour, herd size, herd composition and experience in dairy farming using the OLS method to determine their influence on profit inefficiency (Table 4).Table 4 shows that age had a negative sign in all categories butwas significant only for the medium herd size category. This implies that as age increases, the risk-bearing capacity of farmers decreases, thereby increasing efficiency (Adamu and Bakari, 2015; Acharya et al., 2021).


       
Education had a negative and significant impact on profit inefficiency in case of small (-0.0176), medium (-0.0198), large (-0.0177) and overall (-0.0175) categories of farmers, respectively. Improving farmers’ education helps to enhance profit efficiency. Nganga et al., (2010), Ogunniyi (2011), Kaka et al., (2016), Kumari et al., (2020) and Acharya et al., (2021) all reported similar findings.
               
Herd size and herd composition had a negative and significant impact on profit inefficiency in case of small (-0.0441 and -0.4019); medium (-0.7702 and -0.2986); large (-0.0350 and -1.0381) and overall (-0.0130 and -0.2494) categories of dairy farmers, respectively. This shows that by increasing the number of crossbred cows in a herd leads to increased milk yield and profits.These were similar to the findings Nganga et al., (2010), Kumari et al., (2020), Yilmaz et al., (2020) and Acharya et al., (2021).
       
Experience in dairy farming had a negative and significant impact on inefficiency incase of small (-0.2835), medium (-0.3884) and overall (-0.0220) categories of farmers, while the same was positive and non-significant in case of a large herd size category. It means that profit efficiency will be higher for highly experienced farmers because of their efficient usage, resource allocation, and adoption of new technologies. Rahman (2003), Nganga et al., (2010), Ogunniyi (2011), Sharafat (2013), Kaka et al., (2016), Kumari et al., (2020), Yilmaz et al., (2020) and Acharya et al., (2021) reported similar results.

The findings above reveal that farmers in the study area feed their cattle with green fodder and concentrate on increasing the milk yield of animals, thereby increasing profits.There is a need to enhance access to dairy production inputs and services (feed, veterinary, breeding, training, and credit services) for dairy farmers. Overall, the value of ¡ was 0.7581, indicating that 75.81 per cent of the variation in actual profit from frontier profit occurred due to differences in farmers’ practices in milk production rather than random noise. Dairy farms with the small herd size category experienced the highest variation in efficiency score, followed by the medium category. They were least in the case of the large herd size category. Farmers with higher levels of education, large farm size, greater number of crossbred cows and more experience in dairying tend to have more profit efficiency. Age, education, herd size and experience in dairy farming were important variables that indirectly influenced profit inefficiency. These findings imply that encouraging new farmers, particularly young farmers, to raise dairy cows by adopting better milk-yielding breeds will increase their productivity and, as a result, their profitability. Therefore, policy initiatives aimed at increasing farmers’ market participation rates through training on profitable dairying, better technology and practices to enhance their knowledge and skills, as well as by providing information and other market-related support services; provision of quality feed with subsidies will significantly contribute to profit efficiency and thereby improve the performance of dairy farms.

None.